Simplify the following expression: $q = \dfrac{a^2 - 6a - 16}{a - 8} $
First factor the polynomial in the numerator. $ a^2 - 6a - 16 = (a - 8)(a + 2) $ So we can rewrite the expression as: $q = \dfrac{(a - 8)(a + 2)}{a - 8} $ We can divide the numerator and denominator by $(a - 8)$ on condition that $a \neq 8$ Therefore $q = a + 2; a \neq 8$